Clapeyron vector

The vanishing of the two-phase Clapeyron vector 8ajg (11.151) is now equivalent to... 

Figure 11.10 Schematic representation of co-Clapeyron vector orientations of (a) base T), P) vectors and (b) resultant Clapeyron vectors X) (dotted), illustrating the geometrical condition (11.165a) for coexistence of a (solid line) and /3 (dashed line) phases. The coordinate origin is marked with a small square in each panel. [Vector lengths, angles, ya, and ASap, AVap, values are chosen purely for illustrative purposes the Clapeyron-matching condition cannot be sensibly illustrated in Si-based units for any real system (Sidebar 11.6).]...

The geometrical picture of phase coexistence is most easily sketched in terms of what may be called the Clapeyron vector 2) of each phase ... 

The Clapeyron vector (evidently closely related to the coexistence coordinate a) at saturation cf. Section 11.5) is merely the projection of the GD vector (11.141b) onto the nonsingular space spanned by T), P). In terms of this vector, the coexistence condition (11.154) can be written as the Clapeyron matching condition ... 

For an element in equilibrium with no body forces, the equations of equilibrium were obtained by Lame and Clapeyron (1831). Consider the stresses in a cubic element in equilibrium as shown in Fig. 2.3. Denote 7y as a component of the stress tensor T acting on a plane whose normal is in the direction of e and the resulting force is in the direction of ej. In the Cartesian coordinates in Fig. 2.3, the total force on the pair of element surfaces whose normal vectors are in the direction of ex can be given by... 

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